By Holt Ashley
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Extra info for Aerodynamics of Wings and Bodies
Course, give vanishing disturbances at infinity since this boundary condition belongs to the outer region. We therefore need to match the inner and outer solutions. This can be done in two ways; either one can use the limit matching principle for W or the asymptotic matching principle for <1>. i( =E '¥I x, To illustrate the use of the asymptotic matching principle we first express the two-term outer flow in inner variables, = l,(x). (5-16) W 'o I 85 I <1>0 = Uoo[x + E
St cOIflpletely useless, since in reality the flow will separate and the sImphfied model then loses its validity. The example emphasizes the fact that extreme caution must be exercised when using the physical model to o~tai? approximate ~ngineering results rather than just to gain a general qualItatIve understandmg of the physical situation and the mathematical ~tructure of th~ pr~blem. Consi~erable insight is generally required to Judge when a sImphfied model WIll provide a useful first approximation to an actual physical situation.
Behind the body. In principle one could have instead a region of fairly quiescent flow in the wake, separated from the outer flow by a thin laminar shear layer attached to the laminar boundary layer on a body. However, a free shear layer, lacking the restraining effect of a wall, will be highly unstable and will therefore turn turbulent almost immediately. Because of the momentum loss due to the turbulent mixing in the wake the drag of the body will be quite large. On a thin airfoil at a small angle of attack the boundary layer will separate at the sharp trailing edge but there will be a very small wake so that a good model for the flow is the attached flow with the Kutta condition for the inviscid outer flow determining the circulation.